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Strongly Sublinear Separators and Bounded Asymptotic Dimension for Sphere Intersection Graphs

Authors James Davies, Agelos Georgakopoulos, Meike Hatzel , Rose McCarty

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  • Mathematics of computing → Discrete mathematics
Keywords
  • Intersection graphs
  • strongly sublinear separators
  • asymptotic dimension

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Abstract

In this paper, we consider the class 𝒞^d of sphere intersection graphs in R^d for d ≥ 2. We show that for each integer t, the class of all graphs in 𝒞^d that exclude K_{t,t} as a subgraph has strongly sublinear separators. We also prove that 𝒞^d has asymptotic dimension at most 2d+2.

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James Davies, Agelos Georgakopoulos, Meike Hatzel, and Rose McCarty. Strongly Sublinear Separators and Bounded Asymptotic Dimension for Sphere Intersection Graphs. In 41st International Symposium on Computational Geometry (SoCG 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 332, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.SoCG.2025.36

Author Details

James Davies
  • University of Cambridge, UK
Agelos Georgakopoulos
  • University of Warwick, UK
Meike Hatzel
  • Institute for Basic Science (IBS), Daejeon, South Korea
Rose McCarty
  • Georgia Institute of Technology, Atlanta, GA, USA

Funding

  • Georgakopoulos, Agelos: Supported by EPSRC grants EP/V048821/1 and EP/V009044/1.
  • Hatzel, Meike: The research was supported by the Institute for Basic Science (IBS-R029-C1).
  • McCarty, Rose: Supported by the National Science Foundation under Grant No. DMS-2202961.

Acknowledgements

This research was initiated during the Banff workshop "New Perspectives in Colouring and Structure (24w5272)". We thank Alex Scott for the construction in Observation 8. We thank Louis Esperet for several helpful discussions.

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